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Reinforcement learning and the power law of practice: some analytical results

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  • Ianni, A.

Abstract

Erev and Roth (1998) among others provide a comprehensive analysis of experimental evidence on learning in games, based on a stochastic model of learning that accounts for two main elements: the Law of Effect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially). This note complements this literature by providing an analytical study of the properties of such learning models. Specifically, the paper shows that: (a) up to an error term, the stochastic process is driven by a system of discrete time difference equations of the replicator type. This carries an analogy with Börgers and Sarin (1997), where reinforcement learning accounts only for the Law of Effect. (b) if the trajectories of the system of replicator equations converge sufficiently fast, then the probability that all realizations of the learning process over a possibly infinite spell of time lie within a given small distance of the solution path of the replicator dynamics becomes, from some time on, arbitrarily close to one. Fast convergence, in the form of exponential convergence, is shown to hold for any strict Nash equilibrium of the underlying game.

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Bibliographic Info

Paper provided by Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 0203.

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Date of creation: 01 Jan 2002
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Handle: RePEc:stn:sotoec:0203

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  1. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  2. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  3. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
  4. Barry Sopher & Dilip Mookherjee, 2000. "Learning and Decision Costs in Experimental Constant Sum Games," Departmental Working Papers 199625, Rutgers University, Department of Economics.
  5. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
  6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  7. Sarin, R. & Vahid, F., 1999. "Predicting how People Play Games: a Simple Dynamic Model of Choice," Monash Econometrics and Business Statistics Working Papers 12/99, Monash University, Department of Econometrics and Business Statistics.
  8. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  9. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  10. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
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Cited by:
  1. Peter Dürsch & Albert Kolb & Jörg Oechssler & Burkhard C. Schipper, 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Bonn Econ Discussion Papers bgse31_2005, University of Bonn, Germany.
  2. Antonella Ianni, 2007. "Learning Strict Nash Equilibria through Reinforcement," Economics Working Papers ECO2007/21, European University Institute.
  3. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
  4. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
  5. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer, vol. 43(3), pages 407-430, June.

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